Add custom CORS headers to AppSync OPTIONS preflight request?

I use Sentry and AppSync with lambda resolvers. I figured out how to get sentry distributed tracing hooked up but it requires the sentry-trace-id and baggage headers. The sentry headers aren't being sent because AppSync sets Access-Control-Request-Headers to a restrictive list of allowed headers in the pre-flight OPTIONS response.

There is a way to set the header in a mapping template - https://docs.aws.amazon.com/appsync/latest/devguide/http-helpers-in-utils-http.html but that doesn't affect the OPTIONS response for CORS.

It would be great if there was a way to add more allowed headers for AppSync CORS requests so that I can enable distributed tracing of requests from the frontend to my AppSync resolver lambda functions.